- Email: [email protected]
Kinematic flow model based extreme wind simulation
Journal of Wind Engineering and Industrial Aerodynamics 77&78 (1998) 1—11
Kinematic flow model based extreme wind simulation E. Cheng *, J. Shang Department of Civil Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA HIES, Kailua, HI 96734, USA
Abstract The physical model discussed herein is a simulated air flow moving over a complex terrain with surface roughness. To model such a wind field, the strategy is to apply the numerical solution to an effective boundary-layer kinematic flow model. A geographic information systems (GIS) software is used to manipulate the massive topographic and roughness data over a fine grid system. The results of this application are compared with measured and historical data as well as previous studies. 1998 Elsevier Science Ltd. All rights reserved. PACS: 92.60.Gn Keywords: Kinematic flow; GIS; Complex terrain; Extreme wind
1. Introduction The purpose of this study is to show that a GIS assisted solution applied successfully in modeling strong winds over a complex terrain. Topographical features such as mountains, valleys, hills, canyons, and cliffs often cause drastic changes in local strong winds. Spatial variability of the atmospheric boundary layer flow increases along with the complexity of the terrain. Clearly, a digital elevation model and a detailed land use and land cover digital models are the most effective means of achieving a higher degree of accuracy in a surface wind field modeling. However, the handling of the massive amount of terrain and surface roughness data is a major task. A computerized geographic information systems (GIS) is used in this study to process these data. Wind data on the north shore of Oahu, Hawaii, is used to calibrate the model. Comparisons of historical and simulated strong winds at Honolulu International Airport are illustrated.
* Corresponding author. E-mail: [email protected]. 0167-6105/98/$ — see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 1 2 7 - 5
2
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
2. Basic strategy The dynamics of boundary layer flows has been extensively studied [1—7]. The mass-consistent boundary layer flow model used in this study has also been enhanced by researchers in recent years [8—11]. To further improve the kinematic model, studies on resolving the details of terrain and land cover features are necessary. This involves adjusting the dependent variables until an imposed constraint — the mass consistency, is satisfied. One approach for the analysis of airflow over complex terrain is to generate mass-consistent (i.e. non-divergent) wind fields. An initial wind velocity field, u (“observed” field), is first generated by an interpolation technique on the basis of surface measurements and upper air soundings. The observed field generally does not satisfy continuity condition. The mass-consistent wind field, u (“adjusted” field), must be calculated. The incompressible form of the continuity equation ( u"0) yields the equation
c"! u , (1) where c"u!u is the velocity difference. For the determination of c , it is assumed that the vorticity calculated on the basis of u is equal to the vorticity resulting from u:
;u" ;u . (2) This corresponds to the requirement, ;c"0, which is identically fulfilled if the velocity difference c can be expressed as the gradient of a scalar field j (i.e., c" j). The result is the elliptic equation:
j"! u . (3) The orography is taken into account by transforming this equation to a terrainfollowing coordinate system. Due to terrain inhomogeneity, the resulting equation includes several additional terms with spatially varying coefficients.
3. Governing equations and solutions In the flow model, the terrain-following sigma system [10] is used. The vertical coordinate, p, is defined as z!h(x, y) p, , H(x, y)!h(x, y)
(4)
where h(x, y) is the height of the terrain above mean sea level, and H(x, y) is the height of the boundary layer. In the sigma system, the wind components u, v and w at each point of the grid mesh are replaced by the variables u*, v* and w*, with u*"u (H!h); v*"v (H!h); and w*"w (H!h). The differences between the observed and the adjusted values of u*, v* and w* are minimized on the following
3
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
conditions: *j 2¼ (u*!u*)! "0, & *x *j 2¼ (v*!v*)! "0, & *y *j 2¼ (w*!w*)! "0, 4 *p
(5)
where j is the Lagrange multiplier. ¼ and ¼ are weights assigned to the horizontal & 4 and vertical wind components. They are determined through numerical experiments. The basic equations of the model can be obtained from Eq. (5). The derived equations involving u*, v* and w* are
*u* *u* ¼ # # & *x *y ¼ 4 *v* *v* ¼ # # & *y ¼ *x 4 *w* *w* ¼ # # & *x *y ¼ 4
*u* *u* ¼ " # & *p *y ¼ 4 *v* *v* ¼ " # & *x ¼ *p 4 *w* ¼ * "! & *p ¼ *p 4
*u* * *v* *w* ! # , *p *x *y *p
*v* * *u* *w* ! # , *y *x *p *p
*u* *v* *w* *w* # # # . *x *y *x *y (6)
Eq. (6) is the governing equation for the flow model. The application of the model involves several input variables, such as wind components (u, v) for each input node. The model has to be executed for each hourly observation to produce a record of simulated winds for each of the test nodes. This requires considerable computational time. Computational time can be greatly reduced by using principal component analysis [10], in which an arbitrary set of observed winds is decomposed into a linear combination of independent data sets. This method may be generalized and applied to the generation of wind fields of numerous nodes and observations. If there are n input nodes and m hourly observations for each station, the input wind components (u, v) would define a matrix (M ) as follows: LK u u 2 u 2 u H K v v 2 v 2 v H K v 22 u u 2 u 2 u GH GK , M " G G (7) LK v v 2 v 2 v G G GH GK v 22 G u u 2 u 2 u L L LH LK v v 2 v 2 v L L LH LK
4
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
where i and j stand for the ith input node and the jth hourly observation, respectively, and the individual column vectors are linearly independent. This matrix can be decomposed into a mean vector »M , 2n normalized eigenvectors G e , and a set of time-dependent coefficients a , for m*2n. Therefore, I IH u eI uN L GH " GS # G a (8) IH v eI vN I GH GT G for i"1, 2,2, n; j"1, 2,2, m and k"1, 2,2, 2n, where a is the coefficient of the IH kth eigenvector at period j, and uN , vN are the average wind speed components over all G G the input data sets at the ith node. The kth eigenvector e and the mean vector » can I G be expressed as
e "(eI , eI ,2, eI , eI ,2, eI , eI ), (9) I S T GS GT LS LT »M "(uN , vN ). (10) G G G The coefficients a are the inner products of the input data vector and each of the IH eigenvectors, because the eigenvectors are orthogonal. Therefore, L a " [(u !uN )eI #(v !vN )eI ], (11) IH GH G GS GH G GT G where i"1,2,2,n; j"1, 2,2, m, and k"1, 2,2, 2n. The model then can be executed for the eigenvectors (eN ) and the mean vector (»M ). I G The generated winds (denoted by *) at period j for node r may be calculated as follows:
u* uN * u* L PH " P # PI . a (12) IH v* vN * v* I PH P PI The important advantage of using this generalized principal component analysis is that the full model calculations need not be made for more than a few runs, once for the mean and once for each of the eigenvectors. The reconstructed solutions are obtained by using the appropriate inner products to form the necessary linear combinations of solutions.
4. Application The undisturbed open ocean flow is used to define the initial wind field over the study area. The open ocean flow at ten meters above the mean sea level (10 m amsl) can be considered as uniform flow because the shear layer above the ocean is very shallow. In this study, the lower limit of the modeling field is specified by the topography of the application area, while the upper limit is the top of the boundary layer. Both surfaces are assumed to be rigid and impermeable. The primary factor in modeling wind profile is the determination of wind profile parameters, including power law exponent, shear layer depth and zero-plane displacement. These parameters are dependent upon the terrain and surface roughness. The
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
5
surface roughness zones are characterized by land cover type and topographic features. In other words, the surface roughness at each cell of the area to be modeled is dictated by terrain features (such as valleys, ridges, and plains) and the type of land cover in that cell. This process can be complicated and tedious because there are multitude combinations of land cover types and geographic features. With limited historical records, it is impossible to calibrate all of these parameters. For this reason, certain principles must be established in order to simplify the surface roughness parameterization into a workable form, and at the same time minimize whatever errors may be caused by the simplification. The formulation of these principles is guided by ASCE 7-95 [12] and the results of other relevant studies [13]. The extensive operations of surface roughness parameterization for each cell of the modeled area were performed using the GIS database. In this study, the atmospheric volume is divided into a three-dimensional grid. The vertical direction is subdivided into 10 levels, while the grid in the x—y direction is determined by the application requirements and computing limitations. The requirements for constructing and operating such an airflow model include compiling and manipulating large spatial data sets. They are mainly the topography coverage, developed from the US Geological Survey (USGS) digital elevation model (DEM); and the ground cover categorization, based on the USGS land use and land cover digital data (LULCDD). ARC/INFO [14] is used to process and manipulate the spatial data during model calibration. In using the ARC/INFO, the first step is to transform the two coverages (DEM and LULCDD) into the format used in the boundary-layer flow model. The DEM for the Island of Oahu is mapped into joined lattices and later converted to a point (elevation) and an arc (contour) coverage. Projections from the geographic coordinate system to the Universal Transverse Mercator (UTM) are conducted at this stage. Parallel processing is performed for the LULCDD while polygon coverage for Oahu is formed and overlaid with the DEM coverage. Land cover types are denoted by the Landcover code. The elevation and the landcover coverages are grided. The desired resolution is determined by the requirements of the model and the capacity of the computer. The grided coverages are then linked and converted into forms readable by the program. The second step consists of modifying the program to incorporate the GIS database into the proposed model and parameterizing the wind profile. In executing the model, the simulation output is written in the ARC/INFO data format. Consequently, the modeling results may be graphically presented in the GIS, which is an advantage of integrating GIS into the flow model.
5. Results To calibrate the model, the wind speed and direction at the Kahuku Opana station (Fig. 1) are simulated. The initial conditions for the simulation process are the wind data recorded at the Oyster Farm station (Fig. 1). The duration of this hourly data is from 1 : 00, 22 August 1980 to 24 : 00, 30 August 1980. During this period, the wind direction is generally onshore. Wind speed and direction at the Kahuku Opana
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E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
Fig. 1. Wind stations used on Oahu, Hawaii.
Table 1 Mean and standard deviation of wind data at the Kahuku Opana station (14 m above ground level, 22—30 August 1980) Observed Speed (m/s) Mean Standard deviation
6.44 1.16
Direction (deg.) 84.03 10.86
Previous study [15]
Current model
Speed (m/s)
Speed (m/s)
5.94 1.20
Direction (deg.) 96.97 12.89
6.13 0.88
Direction (deg.) 94.66 11.86
station are simulated under the same initial conditions using the improved flow model and the GIS spatial database. The ground surface elevation in the Kahuku area ranges from 0 to approximately 400 m/amsl. There are several small valleys and ridges in the Kahuku area, and the highest elevation is at the south central portion of the area. The simulated data were compared with measured records and the results obtained from a previous study [15]. The simulated results are very encouraging (Table 1 and Fig. 2). This is especially true between the 60th hour to the 90th hour as indicated in Fig. 2, since the wind directions during this period are mostly northern, resulting in direct wind flow from the Oyster Farm toward Kahuku Opana. This further demonstrates that the improved flow model is more effective in simulating surface roughness as well as terrain effects. The modified model further utilized to model the wind field over the entire Island of Oahu. The simulated strong winds were compared with the historical data as well as the results obtained from previous studies at Honolulu International Airport (the only station having historical data). The surface area of Oahu is about 610 square miles. The landscape is dominated by volcanic landforms (Fig. 3). The island is made
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
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Fig. 2. Comparison of observed and simulated wind speeds at Kahuka Opana with results of previous study [15] for the period from 1 : 00, 22 August 1980 to 24 : 00, 30 August 1980.
Fig. 3. Elevation contour map of Oahu, Hawaii.
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E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
up of two greatly eroded volcanoes, the Koolau and Waianae mountain ranges (Fig. 1). Lava flows from both ranges have joined to create a central plain. Fig. 4 shows the distribution of vegetation and land use on Oahu. Honolulu is the largest city on Oahu. There are other urbanized areas and small towns scattered around the island. Industrial parks are centered around Honolulu and Pearl Harbor and at Barbers Point. Military bases and training areas occupy 26 percent of the island. Sugar and pineapple plantations occupy much of the Leilehua Plateau and extend north to Waialua and south to Ewa. The two mountain ranges are covered with rain forest and shrubs. Based on 15 yr (1950—64) historical data recorded at Honolulu International Airport, long-term (100 yr) hourly wind data were successfully generated by means of a stochastic simulation model [16]. This generated long-term wind data were the basis of input in the island-wind field simulation. The key elements of this simulation procedure are briefly described in the following sequential steps: (1) determine the threshold value and the number of strong winds, v and n , in each G G of the 100 yr generated wind speeds at Honolulu International Airport.
Fig. 4. Land cover and land use map of Oahu, Hawaii.
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
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(2) for each year, use the defined number of strong winds in step (1) as the model input. For a given year i, therefore, n number of strong winds at a project site will be G simulated. (3) repeat step (2) until a desirable number of years is reached. For Honolulu International Airport, the threshold value of strong winds of 13 m/s is selected. This value is the lower limit of the tail quantile of the wind rose at Honolulu International Airport as defined in an earlier study [16]. Based on the procedures described, strong winds were generated by using the GIS integrated boundary layer flow model. The current model results indicated in Fig. 5 are in good agreement with the threshold value based Rayleigh simulation model [17]. In the Rayleigh simulation model, strong winds were generated by a parametric model for fitting the tail quantile of wind rose at Honolulu International Airport with a Rayleigh distribution. The stochastically generated strong winds presented in Fig. 5 are intended for measuring the performance of the current GIS integrated flow model. This stochastic model [16] is not a threshold value based model. This method uses historical wind data to establish Markov transition probabilities at Honolulu International Airport. These probabilities were the guide for producing synthesized wind data time series of a desired period.
Fig. 5. Cumulative distributions of strong winds at Honolulu International Airport, Oahu, Hawaii (at 10 m above ground level).
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The strong winds generated from the modified flow model at Honolulu International Airport are generally in agreement with the historical data collected over the 15 yr period (1950—64).
6. Conclusions A GIS assisted flow model has been demonstrated to simulate wind speed and direction over areas with complex terrain and surface roughness. The results obtained from this study are substantial and encouraging. Further research is needed to generalize this approach.
Acknowledgements Partial support of this study by the National Science Foundation through grant BCS-9122224 is gratefully acknowledged.
References [1] Y. Sasaki, Some basic formalisms in numerical variational analysis, Mon. Weather Rev. 98 (12) (1970) 875—883. [2] F. Kimura, A numerical simulation of local winds and photochemical air pollution (II): application to the Kanto plain, J. Meteorol. Soc. Jpn. 63 (5) (1985) 923—935. [3] F. Kimura, A simulation of wind and air pollution over complex terrain using a hydrostatic numerical model, Atmos. Environ. 23 (4) (1989) 723—730. [4] P. Alpert, B. Getenio, One-level diagnostic modeling of mesoscale surface winds in complex terrain. Part I: comparison with three-dimensional modeling in Israel, Mon. Weather Rev. 116 (1988) 2025—2046. [5] P. Alpert, B. Getenio, One-level diagnostic modeling of mesoscale surface winds in complex terrain. Part II: applicability to short-range forecasting, Mon. Weather Rev. 116 (1988) 2047—2061. [6] H.N. Lee, W.S. Kau, Simulation of three-dimensional wind flow over complex terrain in the atmospheric boundary layer, Boundary-layer Meteorol. 29 (1984) 81—396. [7] D.G. Ross, Diagnostic wind field modeling for complex terrain: model development and testing, J. Appl. Meteorol. 27 (1988) 785—796. [8] M.H. Dickerson, MASCON — a mass consistent atmospheric flux model for regions with complex terrain, J. Appl. Meteorol. 17 (3) (1978) 241—253. [9] C.A. Sherman, A mass — consistent model for wind fields over complex terrain, J. Appl. Meteorol. 17 (3) (1978) 312—319. [10] C.M. Bhumralkar, A practical and economic method for estimating wind characteristics at potential wind energy conversion sites, Sol. Energy 25 (1980) 55—65. [11] R.M. Endlich, F.L. Ludwig, C.M. Bhumralkar, A diagnostic model for estimating winds at potential sites for wind turbines, J. Appl. Meteorol. 21 (10) (1982) 441—1454. [12] American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures, ASCE 7-95, New York, 1996. [13] E. Simiu, R. Scanlan, Wind Effects on Structures, 3rd ed., Wiley, New York, 1996. [14] ESRI, Understanding GIS — the ARC/INFO method, Rev. 7, Environmental Systems Research Institute, Inc., Redlands, CA, 1995.
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[15] D.A. Erasmus, A comparison of simulated and observed boundary-layer winds in an area of complex terrain, J. Climate Appl. Meteorol. 25 (12) (1986) 1842—1852. [16] E.D. Cheng, A.N. Chiu, Extreme winds simulated from short-period records, J. Struct. Eng. ASCE 111 (1) (1985) 77—94. [17] E.D. Cheng, A.N. Chiu, Estimating design wind speeds from short-term, records, Proc. 3rd Asia—Pacific Symp. on Wind Engineering, Hong Kong, 1993, pp. 519—524.
Kinematic flow model based extreme wind simulation E. Cheng *, J. Shang Department of Civil Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA HIES, Kailua, HI 96734, USA
Abstract The physical model discussed herein is a simulated air flow moving over a complex terrain with surface roughness. To model such a wind field, the strategy is to apply the numerical solution to an effective boundary-layer kinematic flow model. A geographic information systems (GIS) software is used to manipulate the massive topographic and roughness data over a fine grid system. The results of this application are compared with measured and historical data as well as previous studies. 1998 Elsevier Science Ltd. All rights reserved. PACS: 92.60.Gn Keywords: Kinematic flow; GIS; Complex terrain; Extreme wind
1. Introduction The purpose of this study is to show that a GIS assisted solution applied successfully in modeling strong winds over a complex terrain. Topographical features such as mountains, valleys, hills, canyons, and cliffs often cause drastic changes in local strong winds. Spatial variability of the atmospheric boundary layer flow increases along with the complexity of the terrain. Clearly, a digital elevation model and a detailed land use and land cover digital models are the most effective means of achieving a higher degree of accuracy in a surface wind field modeling. However, the handling of the massive amount of terrain and surface roughness data is a major task. A computerized geographic information systems (GIS) is used in this study to process these data. Wind data on the north shore of Oahu, Hawaii, is used to calibrate the model. Comparisons of historical and simulated strong winds at Honolulu International Airport are illustrated.
* Corresponding author. E-mail: [email protected]. 0167-6105/98/$ — see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 1 2 7 - 5
2
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
2. Basic strategy The dynamics of boundary layer flows has been extensively studied [1—7]. The mass-consistent boundary layer flow model used in this study has also been enhanced by researchers in recent years [8—11]. To further improve the kinematic model, studies on resolving the details of terrain and land cover features are necessary. This involves adjusting the dependent variables until an imposed constraint — the mass consistency, is satisfied. One approach for the analysis of airflow over complex terrain is to generate mass-consistent (i.e. non-divergent) wind fields. An initial wind velocity field, u (“observed” field), is first generated by an interpolation technique on the basis of surface measurements and upper air soundings. The observed field generally does not satisfy continuity condition. The mass-consistent wind field, u (“adjusted” field), must be calculated. The incompressible form of the continuity equation ( u"0) yields the equation
c"! u , (1) where c"u!u is the velocity difference. For the determination of c , it is assumed that the vorticity calculated on the basis of u is equal to the vorticity resulting from u:
;u" ;u . (2) This corresponds to the requirement, ;c"0, which is identically fulfilled if the velocity difference c can be expressed as the gradient of a scalar field j (i.e., c" j). The result is the elliptic equation:
j"! u . (3) The orography is taken into account by transforming this equation to a terrainfollowing coordinate system. Due to terrain inhomogeneity, the resulting equation includes several additional terms with spatially varying coefficients.
3. Governing equations and solutions In the flow model, the terrain-following sigma system [10] is used. The vertical coordinate, p, is defined as z!h(x, y) p, , H(x, y)!h(x, y)
(4)
where h(x, y) is the height of the terrain above mean sea level, and H(x, y) is the height of the boundary layer. In the sigma system, the wind components u, v and w at each point of the grid mesh are replaced by the variables u*, v* and w*, with u*"u (H!h); v*"v (H!h); and w*"w (H!h). The differences between the observed and the adjusted values of u*, v* and w* are minimized on the following
3
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
conditions: *j 2¼ (u*!u*)! "0, & *x *j 2¼ (v*!v*)! "0, & *y *j 2¼ (w*!w*)! "0, 4 *p
(5)
where j is the Lagrange multiplier. ¼ and ¼ are weights assigned to the horizontal & 4 and vertical wind components. They are determined through numerical experiments. The basic equations of the model can be obtained from Eq. (5). The derived equations involving u*, v* and w* are
*u* *u* ¼ # # & *x *y ¼ 4 *v* *v* ¼ # # & *y ¼ *x 4 *w* *w* ¼ # # & *x *y ¼ 4
*u* *u* ¼ " # & *p *y ¼ 4 *v* *v* ¼ " # & *x ¼ *p 4 *w* ¼ * "! & *p ¼ *p 4
*u* * *v* *w* ! # , *p *x *y *p
*v* * *u* *w* ! # , *y *x *p *p
*u* *v* *w* *w* # # # . *x *y *x *y (6)
Eq. (6) is the governing equation for the flow model. The application of the model involves several input variables, such as wind components (u, v) for each input node. The model has to be executed for each hourly observation to produce a record of simulated winds for each of the test nodes. This requires considerable computational time. Computational time can be greatly reduced by using principal component analysis [10], in which an arbitrary set of observed winds is decomposed into a linear combination of independent data sets. This method may be generalized and applied to the generation of wind fields of numerous nodes and observations. If there are n input nodes and m hourly observations for each station, the input wind components (u, v) would define a matrix (M ) as follows: LK u u 2 u 2 u H K v v 2 v 2 v H K v 22 u u 2 u 2 u GH GK , M " G G (7) LK v v 2 v 2 v G G GH GK v 22 G u u 2 u 2 u L L LH LK v v 2 v 2 v L L LH LK
4
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
where i and j stand for the ith input node and the jth hourly observation, respectively, and the individual column vectors are linearly independent. This matrix can be decomposed into a mean vector »M , 2n normalized eigenvectors G e , and a set of time-dependent coefficients a , for m*2n. Therefore, I IH u eI uN L GH " GS # G a (8) IH v eI vN I GH GT G for i"1, 2,2, n; j"1, 2,2, m and k"1, 2,2, 2n, where a is the coefficient of the IH kth eigenvector at period j, and uN , vN are the average wind speed components over all G G the input data sets at the ith node. The kth eigenvector e and the mean vector » can I G be expressed as
e "(eI , eI ,2, eI , eI ,2, eI , eI ), (9) I S T GS GT LS LT »M "(uN , vN ). (10) G G G The coefficients a are the inner products of the input data vector and each of the IH eigenvectors, because the eigenvectors are orthogonal. Therefore, L a " [(u !uN )eI #(v !vN )eI ], (11) IH GH G GS GH G GT G where i"1,2,2,n; j"1, 2,2, m, and k"1, 2,2, 2n. The model then can be executed for the eigenvectors (eN ) and the mean vector (»M ). I G The generated winds (denoted by *) at period j for node r may be calculated as follows:
u* uN * u* L PH " P # PI . a (12) IH v* vN * v* I PH P PI The important advantage of using this generalized principal component analysis is that the full model calculations need not be made for more than a few runs, once for the mean and once for each of the eigenvectors. The reconstructed solutions are obtained by using the appropriate inner products to form the necessary linear combinations of solutions.
4. Application The undisturbed open ocean flow is used to define the initial wind field over the study area. The open ocean flow at ten meters above the mean sea level (10 m amsl) can be considered as uniform flow because the shear layer above the ocean is very shallow. In this study, the lower limit of the modeling field is specified by the topography of the application area, while the upper limit is the top of the boundary layer. Both surfaces are assumed to be rigid and impermeable. The primary factor in modeling wind profile is the determination of wind profile parameters, including power law exponent, shear layer depth and zero-plane displacement. These parameters are dependent upon the terrain and surface roughness. The
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
5
surface roughness zones are characterized by land cover type and topographic features. In other words, the surface roughness at each cell of the area to be modeled is dictated by terrain features (such as valleys, ridges, and plains) and the type of land cover in that cell. This process can be complicated and tedious because there are multitude combinations of land cover types and geographic features. With limited historical records, it is impossible to calibrate all of these parameters. For this reason, certain principles must be established in order to simplify the surface roughness parameterization into a workable form, and at the same time minimize whatever errors may be caused by the simplification. The formulation of these principles is guided by ASCE 7-95 [12] and the results of other relevant studies [13]. The extensive operations of surface roughness parameterization for each cell of the modeled area were performed using the GIS database. In this study, the atmospheric volume is divided into a three-dimensional grid. The vertical direction is subdivided into 10 levels, while the grid in the x—y direction is determined by the application requirements and computing limitations. The requirements for constructing and operating such an airflow model include compiling and manipulating large spatial data sets. They are mainly the topography coverage, developed from the US Geological Survey (USGS) digital elevation model (DEM); and the ground cover categorization, based on the USGS land use and land cover digital data (LULCDD). ARC/INFO [14] is used to process and manipulate the spatial data during model calibration. In using the ARC/INFO, the first step is to transform the two coverages (DEM and LULCDD) into the format used in the boundary-layer flow model. The DEM for the Island of Oahu is mapped into joined lattices and later converted to a point (elevation) and an arc (contour) coverage. Projections from the geographic coordinate system to the Universal Transverse Mercator (UTM) are conducted at this stage. Parallel processing is performed for the LULCDD while polygon coverage for Oahu is formed and overlaid with the DEM coverage. Land cover types are denoted by the Landcover code. The elevation and the landcover coverages are grided. The desired resolution is determined by the requirements of the model and the capacity of the computer. The grided coverages are then linked and converted into forms readable by the program. The second step consists of modifying the program to incorporate the GIS database into the proposed model and parameterizing the wind profile. In executing the model, the simulation output is written in the ARC/INFO data format. Consequently, the modeling results may be graphically presented in the GIS, which is an advantage of integrating GIS into the flow model.
5. Results To calibrate the model, the wind speed and direction at the Kahuku Opana station (Fig. 1) are simulated. The initial conditions for the simulation process are the wind data recorded at the Oyster Farm station (Fig. 1). The duration of this hourly data is from 1 : 00, 22 August 1980 to 24 : 00, 30 August 1980. During this period, the wind direction is generally onshore. Wind speed and direction at the Kahuku Opana
6
E. Cheng, J. Shang/J. Wind Eng. Ind. Aerodyn. 77&78 (1998) 1–11
Fig. 1. Wind stations used on Oahu, Hawaii.
Table 1 Mean and standard deviation of wind data at the Kahuku Opana station (14 m above ground level, 22—30 August 1980) Observed Speed (m/s) Mean Standard deviation
6.44 1.16
Direction (deg.) 84.03 10.86
Previous study [15]
Current model
Speed (m/s)
Speed (m/s)
5.94 1.20
Direction (deg.) 96.97 12.89
6.13 0.88
Direction (deg.) 94.66 11.86
station are simulated under the same initial conditions using the improved flow model and the GIS spatial database. The ground surface elevation in the Kahuku area ranges from 0 to approximately 400 m/amsl. There are several small valleys and ridges in the Kahuku area, and the highest elevation is at the south central portion of the area. The simulated data were compared with measured records and the results obtained from a previous study [15]. The simulated results are very encouraging (Table 1 and Fig. 2). This is especially true between the 60th hour to the 90th hour as indicated in Fig. 2, since the wind directions during this period are mostly northern, resulting in direct wind flow from the Oyster Farm toward Kahuku Opana. This further demonstrates that the improved flow model is more effective in simulating surface roughness as well as terrain effects. The modified model further utilized to model the wind field over the entire Island of Oahu. The simulated strong winds were compared with the historical data as well as the results obtained from previous studies at Honolulu International Airport (the only station having historical data). The surface area of Oahu is about 610 square miles. The landscape is dominated by volcanic landforms (Fig. 3). The island is made
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Fig. 2. Comparison of observed and simulated wind speeds at Kahuka Opana with results of previous study [15] for the period from 1 : 00, 22 August 1980 to 24 : 00, 30 August 1980.
Fig. 3. Elevation contour map of Oahu, Hawaii.
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up of two greatly eroded volcanoes, the Koolau and Waianae mountain ranges (Fig. 1). Lava flows from both ranges have joined to create a central plain. Fig. 4 shows the distribution of vegetation and land use on Oahu. Honolulu is the largest city on Oahu. There are other urbanized areas and small towns scattered around the island. Industrial parks are centered around Honolulu and Pearl Harbor and at Barbers Point. Military bases and training areas occupy 26 percent of the island. Sugar and pineapple plantations occupy much of the Leilehua Plateau and extend north to Waialua and south to Ewa. The two mountain ranges are covered with rain forest and shrubs. Based on 15 yr (1950—64) historical data recorded at Honolulu International Airport, long-term (100 yr) hourly wind data were successfully generated by means of a stochastic simulation model [16]. This generated long-term wind data were the basis of input in the island-wind field simulation. The key elements of this simulation procedure are briefly described in the following sequential steps: (1) determine the threshold value and the number of strong winds, v and n , in each G G of the 100 yr generated wind speeds at Honolulu International Airport.
Fig. 4. Land cover and land use map of Oahu, Hawaii.
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(2) for each year, use the defined number of strong winds in step (1) as the model input. For a given year i, therefore, n number of strong winds at a project site will be G simulated. (3) repeat step (2) until a desirable number of years is reached. For Honolulu International Airport, the threshold value of strong winds of 13 m/s is selected. This value is the lower limit of the tail quantile of the wind rose at Honolulu International Airport as defined in an earlier study [16]. Based on the procedures described, strong winds were generated by using the GIS integrated boundary layer flow model. The current model results indicated in Fig. 5 are in good agreement with the threshold value based Rayleigh simulation model [17]. In the Rayleigh simulation model, strong winds were generated by a parametric model for fitting the tail quantile of wind rose at Honolulu International Airport with a Rayleigh distribution. The stochastically generated strong winds presented in Fig. 5 are intended for measuring the performance of the current GIS integrated flow model. This stochastic model [16] is not a threshold value based model. This method uses historical wind data to establish Markov transition probabilities at Honolulu International Airport. These probabilities were the guide for producing synthesized wind data time series of a desired period.
Fig. 5. Cumulative distributions of strong winds at Honolulu International Airport, Oahu, Hawaii (at 10 m above ground level).
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The strong winds generated from the modified flow model at Honolulu International Airport are generally in agreement with the historical data collected over the 15 yr period (1950—64).
6. Conclusions A GIS assisted flow model has been demonstrated to simulate wind speed and direction over areas with complex terrain and surface roughness. The results obtained from this study are substantial and encouraging. Further research is needed to generalize this approach.
Acknowledgements Partial support of this study by the National Science Foundation through grant BCS-9122224 is gratefully acknowledged.
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